Adaptive FPGA-Based Mixed-Radix NTT Architectures with Classical and Quantum Evaluation for CRYSTALS-Kyber

The imminent threat of large-scale quantum computers motivates the deployment of post-quantum cryptography (PQC). CRYSTALS-Kyber, a leading lattice-based Key Encapsulation Mechanism, relies heavily on Number Theoretic Transform (NTT) operations, which remain a major performance and resource bottleneck. This paper presents a cross-platform NTT evaluation framework for CRYSTALS-Kyber, centered on an adaptive FPGA-based mixed-radix accelerator supporting radix-2, radix-4, and radix-8 configurations, together with comparative classical implementations and exploratory quantum-circuit prototypes. Classical evaluations show that an iterative Cooley–Tukey implementation outperforms a matrix-based baseline (≈3.6× faster for the forward NTT, ≈6.3× faster for the inverse NTT). Quantum prototypes implemented in Qiskit demonstrate proof-of-concept QFT-based NTT constructions under classical simulation environments, highlighting circuit-depth growth and noise sensitivity rather than practical hardware acceleration. The proposed FPGA design, based on a Xilinx Virtex UltraScale+ platform, employs an adaptive radix controller, LUT-based twiddle management, and Montgomery/Barrett modular arithmetic. Montgomery reduction provides superior timing and area trade-offs, with an estimated Fmax of up to 231.48 MHz and only 5 DSPs for radix-2. At the same time, radix-2 offers the best resource/performance balance with a latency of approximately 32,804 cycles. The hybrid approach strikes a balance between near-term FPGA practicality and long-term quantum potential while preserving Kyber’s MLWE-based security. Experimental results and comparative analysis indicate that the adaptive design substantially reduces resource usage and timing overhead compared to recent HLS-based NTT accelerators.